The striker has been hit with a knee injury.
"Destiny (Udogie) has trained but Pedro is probably a week away," said manager Postecoglou.
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"Richarlison is out for three to four weeks. He picked up a knee injury last game and Sess is out, so still down a couple of numbers.
"Richy is disappointed because he's been a key contributor, but that has been how our season has gone.
"With Sess, it is a tough one. He has worked hard to come back and it is always more challenging when it happens as a series of events."